Uncertainty and Game Theory

A. Economics of Risk and Uncertainty

1. Economic life is full of uncertainty. Consumers face uncertain incomes and employment patterns as well as the threat of catastrophic losses; businesses have uncertain costs, and their revenues contain uncertainties about price and production.

2. In well-functioning markets, arbitrage, speculation, and insurance help smooth out the unavoidable risks. Speculators are people who buy and sell assets or commodities with an eye to making profits on price differentials across markets. They move goods across regions from low-price to high-price markets, across time from periods of abundance to periods of scarcity, and even across uncertain states of nature to periods when chance makes goods scarce.

3. The profit-seeking action of speculators and arbitragers tends to create certain equilibrium patterns of price over space and time. These market equilibria are zero-profit outcomes where the marginal costs and marginal utilities in different regions, times, or uncertain states of nature are in balance. To the extent that speculators moderate price and consumption instability, they are part of the invisible-hand mechanism that performs the socially useful function of reallocating goods from feast times (when prices are low) to famine times (when prices are high).

4. Speculative markets allow individuals to hedge against unwelcome risks. The economic principle of risk aversion, which derives from diminishing marginal utility, implies that individuals will not accept risky situations with zero expected value. Risk aversion implies that people will buy insurance to reduce the disastrous declines in utility from fire, death, or other calamities.

5. Insurance and risk spreading tend to stabilize consumption in different states of nature. Insurance takes large individual risks and spreads them so broadly that they become acceptable to a large number of individuals. Insurance is beneficial because, by helping to equalize consumption across different uncertain states, it raises the expected level of utility.

6. The conditions for operation of efficient insurance markets are stringent: there must be large numbers of independent events, with little chance of moral hazard or adverse selection. When market failures such as adverse selection arise, prices can become distorted or markets may simply not exist. If private insurance markets fail, the government may step in to provide social insurance. Even in the most laissez-faire of advanced market economies today, governments insure against unemployment and health risks in old age.

B. Game Theory

7. Economic life contains many situations of strategic interaction among firms, households, governments, or others. Game theory analyzes the way that two or more parties, who interact in an arena such as a market, choose actions or strategies that jointly affect each participant.

8. The basic structure of a game includes the players, who have different actions or strategies, and the payoffs, which describe the profits or other benefits that the players obtain in each outcome. The key new concept is the payoff table of a game, which shows the strategies and the payoffs or profits of the different players.

9. The key to choosing strategies in game theory is for players to think through both their own and their opponent’s goals, never forgetting that the other side is doing the same. When playing a game in economics or any other field, assume that your opponent will choose his or her best option. Then pick your strategy so as to maximize your benefit, always assuming that your opponent is similarly analyzing your options.

10. Sometimes a dominant strategy is available, one that is best no matter what the opposition does. More often, we find the Nash equilibrium (or noncooperative equilibrium) a useful equilibrium concept. A Nash equilibrium is one in which no player can improve his or her payoff given the other player’s strategy. Sometimes, parties can collude or cooperate, which produces the cooperative equilibrium.

11. A Nash equilibrium produces an efficient outcome in Adam Smith’s invisible-hand game. Here, noncollusive firms produce at prices equal to marginal costs, and the noncooperative equilibrium is efficient. In such situations, cooperation leads to inefficient production.

12. Sometimes, however, noncooperative behavior leads to social ruin, as when competitors pollute the planet or engage in dangerous arms races. Winner-take-all games, such as lawsuits or athletic contests, can induce the entry of too many contestants and increase the inequality of fame and incomes.